We propose to further develop and evaluate several new and exciting ultrasound imaging and tissue characterization algorithms for application to cancer detection and diagnosis. Present B-scan ultrasound methods provide a spatial resolution typically of about 1 to 3 mm at 3 Mhz for depths of 1 to 10 cm, which degrades further with depth. Characterization of tissue by absorption from B-scan data has a resolution dictated by theory of more than 1 cm. Ultrasound transmission tomography shows good quantitative accuracy and specificity for cancer detection, but poor spatial resolution of about 1 cm. Our new imaging algorithms overcome the limitations of the above methods and provide performance at or near theoretical limits. In particular, our synthetic focus algorithms provide spatial resolution approaching 1/2 to 1/4 mm, (i.e., one-half wavelength) with semiquantitative accuracy. Frequency extrapolation and finite difference algorithms provide high resolution and quantitative accuracy or transmission imaging for data with good signal-to-noise ratios. An additional breakthrough in algorithm implementation now permits fast computation of the inverse scattering solution of the exact (not linearized) Helmholtz wave equation for a visco-elastic fluid model of tissue with inhomogeneous density p, speed of sound c, and absorption a, properties. This solution, as computed, using the method of moments with sinc basis functions, is robust (noise tolerant and stable), has extremely high-spatial resolution and provides highly accurate quantitative images of the above defined tissue parameters p, c, a. A similar, but perhaps faster, converging solution to the Riccati wave equation has also been formulated. Since results to date are excellent, a prototype electronically addressed transducer array scanner will be built to obtain more accurate data faster and to help evaluate a designs for full-scale clinical breast and abdominal scanners.